Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN: 9781337278461
Author: Ron Larson
Publisher: Cengage Learning
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Find the equation of a tangent line to a curve given by
f(x) = 3x3 + 2x2 +x+1at x =1.
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Transcribed Image Text:Find the equation of a tangent line to a curve given by f(x) = 3x3 + 2x2 +x+1at x =1.
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Step 1

We first find the slope of the tangent for which we need derivative of f(x).  Differentiating f(x) w.r.t. x we get:

Calculus homework question answer, Step 1, Image 1
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Step 2

Now, slope is the value of f’(x) at the given point x = 1.

Calculus homework question answer, Step 2, Image 1
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Step 3

Now, to find any one point on the tangent line, we consider the fact that tangent line is drawn at x=1. This point also lies on the curve and hence its y-coordinate is the value of f(x) at x=1. We get:

Calculus homework question answer, Step 3, Image 1
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