If f(x) = 5x² – 4x, find f'(2) and use it to find an equation of the tangent line to the parabola y = 5x2 - 4x at the point (2, 12).%3Df'(2)%3Dy(x)%DAdditional Materials

Answered: If f(x) = 5x2 - 4x, find f'(2) and use…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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If f(x) = 5x² – 4x, find f'(2) and use it to find an equation of the tangent line to the parabola y = 5x2 - 4x at the point (2, 12).
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f'(2)
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y(x)
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Expert Solution

Step 1

$G i v e n t h a t f (x) = 5 x^{2} - 4 x T o f i n d : e q u a t i o n o f \tan g e n t a t p o i n t (2, 12) a n d f' (2) S o l u t i o n : f (x) = 5 x^{2} - 4 x f' (x) = 10 x - 4 f' (2) = 10 \times 2 - 4 = 16 s l o p e = \frac{d y}{d x} = f' (x) e q u a t i o n o f \tan g e n t a t p o i n t (a, b) y - b = \frac{d y}{d x} (x - a) a = 2, b = 12, \frac{d y}{d x} = f' (2) = 16 y - 12 = 16 (x - 2) y = 16 x - 20$