Show your complete solution. Activity 1. Find an equation of the tangent line to the graph of the equation at thegiven point.y = 16 – x23;2. f(x) = 3x2 + 9x; (0,0)3. g(x) = x3 + 3;1.(3, 7)(0,3)Activity 2. Find f'(x) in the following.1. f(x) = 3x2 + 2x%3D2. f(x) =!3. f(x) =X-2

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Answered: Activity 1. Find an equation of the…

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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Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(f(x)). y 15 10 5 -2 4 6. 10 (a) Write an equation for h'(x) in terms of f(x), g(x), f'(x), and g'(x). O h'(x) = g'(f'(x))f'(x) O h'(x) = g'(f(x))f'(x) h'(x) = f'(g'(x))g'(x) h'(x) = f'(g(x))gʻ(x) O h'(x) = f'(g'(x))g(x) O h'(x) = g'(f'(x))f(x) Find h'(3). (If an answer does not exist, enter DNE.) (b) Write an equation for s'(x) in terms of f(x), g(x), f'(x), and g'(x). O s'(x) = f'(g(x))g'(x) O s'(x) = g'(f'(x))F'(x) O s'(x) = f'(g'(x))g'(x) s'(x) = g'(f(x))f'(x) s'(x) = f'(g'(x))g(x) s'(x) = g'(f'(x)){x) Find s'(7). (If an answer does not exist, enter DNE.)
Suppose f(5) - 9 and f'(5) = - 3. - = An object moves along the curve y³ – 3x² ƒ(x) – 5x 649. For an animation, Madison needs the equation of the line tangent to the curve at the point where x = 5. The equation of the tangent line needed by Madison is
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6. The graphs of f(x) = x² + 5 and g(x) = -x² + 2 share two common tangent lines. Find the equations of these tangents. Express your equations in y=mx+b form.
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Activity 1. Find an equation of the tangent lim given point. 1. y = 16 - x2; 2. f(x) = 3x2 + 9x; (0,0) 3. g(x) = x3 +3; (3, 7) %3D (0,3) %3D