Finding the Tangent Line at a Point
Read this topicExplanations 3
- Tangent line = a straight line that barely passes through a curve. Tangent lines are equal to zero when the line change from increase to decrease or the opposite way around. Thi…
By John LI, James Cleveland, Victor Wang
- (Video) Finding the Linearization at a Point by PatrickJMT Here's a video by patrickJMT showing you how to find a tangent line approximation, or linearization, of a function. Wh…
By Alex Federspiel
- (Videos) Finding a Linear Approximation by PatrickJMT Here's a video by patrickJMT where he goes through an example of finding the linearization of a function at a point. In the…
By Alex Federspiel, Victor Wang
Problems 6
- Note that e0=1e^0=1e0=1, and the derivative of exe^xex at x=0x=0x=0 is 111. Using this information, the value of e0.1e^{0.1}e0.1 can be estimated to:
- Let aaa be the real number such that the curve y=exy = e^xy=ex is tangent to the curve y=ax2y = ax^2y=ax2 in the coordinate plane. Find ln(4a)\ln(4a)ln(4a). Source: HMMT Februa…
- 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 linearization to estimate e0.07e^{0.07}e0.07.
- Use linearization to estimate tan(4)\tan(4)tan(4).