Question

Assume that f and g are differentiable functions, with h(x)=g(f(x)). Suppose that the slope of the tangent line to the graph of f at the point (4,7) is 33, and the slope of the tangent line to the graph of g at the point (7,9) is −2−2. Determine the slope of the tangent line to the graph of h at x=4.

Name: assume that f and g are differentiable functions with hxgfx suppose that the slope of the tangent line to the graph of f at the point 47 is 33 and the slope of the tangent line to the graph 64795
Uploaded: 2023-02-17T18:54:49-08:00
Duration: 1 min 20 s
Channel: Aman Gupta
Description: assume that f and g are differentiable functions with hxgfx suppose that the slope of the tangent line to the graph of f at the point 47 is 33 and the slope of the tangent line to the graph 64795

          Assume that f and g are differentiable
functions, with h(x)=g(f(x)). Suppose that the slope of the tangent
line to the graph of f at the
point (4,7) is 33, and the slope of the tangent line
to the graph of g at the
point (7,9) is −2−2. Determine the slope of the
tangent line to the graph of h at x=4.

Added by Alexis B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Aman Gupta

02/17/2023

Step 1

h'(4)=-2?2h(4)+3h(7) The derivative of h at x=4 is ?2?2h(4)+3h(7), which is (3+7)h. Show more…

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Assume that f and g are differentiable functions, with h(x)=g(f(x)). Suppose that the slope of the tangent line to the graph of f at the point (4,7) is 33, and the slope of the tangent line to the graph of g at the point (7,9) is −2−2. Determine the slope of the tangent line to the graph of h at x=4.