Derivatives of Polynomials
Read this topicExplanations 3
- There are many steps to differentiating polynomials. The first step would be to idenify the variables and the constants. The second step is to multiply the coefficents of each v…
By naya nazario
- To differentiate polynomials you have to first identify the variable and constant terms in the equation. y = 6x^3 + 7x^2 + 4x + 2 The variable terms are 6x3, 7x^2, and 4x The co…
By Isis Vazquez, Chyna White
- The first form of Power Rule was used by Bonaventura Cavalieri in the 17 century and was later improved by Newton and Leibniz who was both working individually. The power rule i…
By Howei
Problems 31
- Find the instantaneous rate of change for the function f(x)=4x2+4x−3f(x)=4x^2+4x−3f(x)=4x2+4x−3 at x=5x=5x=5.
- Let aaa be a real number and consider the function f(x)=x4−x3−x2+ax+1f(x) = x^4 - x^3 - x^2 + ax + 1f(x)=x4−x3−x2+ax+1. Suppose fff has a local minimum at aaa, and f(a)=af(a) = …
- What's the slope of the tangent line at the unique point of inflection of the function f(x)=x3−3x2+6x+2000f(x) = x^3 - 3x^2 + 6x + 2000f(x)=x3−3x2+6x+2000? Source: HMMT February…
- Which of the following are critical points of f(x)=x4−2x2+2f(x) = x^4 - 2x^2 + 2f(x)=x4−2x2+2?
- Classify the concavity of f(x)=x3−5x2f(x) = x^3 - 5x^2f(x)=x3−5x2 at x=1x=1x=1.
- Differentiate f(x)=x4−3x+7f(x) = x^4 - 3x + 7f(x)=x4−3x+7.
- (High School National Science Bowl 2015, Double Elimination Round 8 #22 Bonus) To the nearest integer, what is 2.9852.98^52.985? Remember that, since this is a Science Bowl ques…
- Suppose that f(x)=x3−3x+1f(x) = x^3 - 3x + 1f(x)=x3−3x+1. Find f′(2)f'(2)f′(2).
- If f(x)=x8−7x7+9x4−3x5+2x−1f(x) = x^8 - 7x^7 + 9x^4 - 3x^5 + 2x - 1f(x)=x8−7x7+9x4−3x5+2x−1, compute f(8)(x)f^{(8)}(x)f(8)(x).
- If h(t)=t2−3t+4h(t) = t^2 - 3t + 4h(t)=t2−3t+4, find h′(2)h'(2)h′(2).
- Determine the intervals on which the function f(x)=x3−6x2−15x+20f(x)=x^3-6x^2-15x+20f(x)=x3−6x2−15x+20 is increasing and decreasing.
- The cost of producing a unit of goods for a factory is C(x)=3000+15x+0.03x2C(x)=3000+15x+0.03x^2C(x)=3000+15x+0.03x2. Find the instantaneous rate of change when x=300x=300x=300.
- You and a friend are planning a hike through some mountains. You know the equation for your elevation is as follows, E(t)=150x2−7.5x3E(t)=150x^2-7.5x^3E(t)=150x2−7.5x3 where xxx…
- Find the instantaneous rate of change for f(x)=5x2−6x+9f(x)=5x^2-6x+9f(x)=5x2−6x+9 at x=11x=11x=11.
- Find the instantaneous rate of change for f(x)=8000+240x−1.25x2f(x)=8000+240x-1.25x^2f(x)=8000+240x−1.25x2 at x=50x=50x=50.
- The instantaneous rate of change for f(x)=ax2−40x+76f(x)=ax^2-40x+76f(x)=ax2−40x+76 is 888 at x=6x=6x=6. What is aaa?
- Let f(x)=4x5+3x3−7f(x)=4x^5+3x^3-7f(x)=4x5+3x3−7. Find f′′(x)f''(x)f′′(x).
- Let f(x)=4x5+3x3−7f(x)=4x^5+3x^3-7f(x)=4x5+3x3−7. Find f′′′(x)f'''(x)f′′′(x).
- Let f(x)=4x5+3x3−7f(x)=4x^5+3x^3-7f(x)=4x5+3x3−7. Find f(4)(x)f^{(4)}(x)f(4)(x).
- Let f(x)=4x5+3x3−7f(x)=4x^5+3x^3-7f(x)=4x5+3x3−7. Find f(5)(x)f^{(5)}(x)f(5)(x).
- Let f(x)=4x5+3x3−7f(x)=4x^5+3x^3-7f(x)=4x5+3x3−7. Find f(6)(x)f^{(6)}(x)f(6)(x).
- Find the linear approximation of f(x)=x5+4x4f(x)=x^5+4x^4f(x)=x5+4x4 at a=−1a=-1a=−1.
- Use linear approximation to estimate (2.001)4(2.001)^4(2.001)4.
- Use differentials to estimate (2.016)5(2.016)^5(2.016)5.
- Find the inflection point(s) of f(x)=2x3−24x2+5x+3f(x)=2x^3-24x^2+5x+3f(x)=2x3−24x2+5x+3
- Find where the equation is concave upward and downward f(x)=2x3−24x2+5x+3f\left(x\right)=2x^3-24x^2+5x+3f(x)=2x3−24x2+5x+3
- A particle follows a straight path. Its distance is given by d(t)=5+3t−0.75t2d(t)=5+3t-0.75t^2d(t)=5+3t−0.75t2 where ddd is the distance in meters and ttt is the time in seconds…
- Find the intervals on which the function f(x)=12x4−2x3−52x2+15xf(x)=\frac{1}{2}x^4-2x^3-\frac{5}{2}x^2+15xf(x)=21x4−2x3−25x2+15x is increasing and decreasing.
- What are the critical points for the function f(x)=3x3−4x+19f(x)=3x^3-4x+19f(x)=3x3−4x+19
- What are the critical points for the function f(x)=5x2+8x+11f(x)=5x^2+8x+11f(x)=5x2+8x+11
- What is the sum of the critical values of the function f(x)=12x4+4x3−4x2−48x+ef(x)=\frac12x^4+4x^3-4x^2-48x+ef(x)=21x4+4x3−4x2−48x+e