Consider the curve y=x-x^5 . Find the slope of the tangent line to the curve at the point...

Question:

Consider the curve {eq}y=x-x^5 {/eq}. Find the slope of the tangent line to the curve at the point (1,0). Find the equation of the tangent line.

Equation of a Tangent Line:

Suppose a tangent line crosses the curve {eq}f(x) {/eq} at the point {eq}(a,f(a)) {/eq}.

At that point, the slope of both the tangent line and the curve is {eq}f'(a) {/eq}.

Hence, the equation of the tangent line is given by

{eq}y - f(a) = f'(a)(x-a) {/eq}

Answer and Explanation:

Calculate first the slope of the desired tangent line by deriving {eq}f(x) {/eq} and then substituting in {eq}x = 1 {/eq}:

{eq}\begin{align*} f(x)...

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Slopes of Tangent & Secant Lines

from TExES Mathematics 4-8 Exam (115): Study Guide & Review

Chapter 18 / Lesson 6
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