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 3, and the slope of the tangent line to the graph of g at the point (7, 9) is -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 hx gfx suppose that the slope of the tangent line to the graph of f at the point 4 7 is 3 and the slope of the tangent line to the graph 51311
Uploaded: 2022-10-11T18:51:02-08:00
Duration: 2 min 14 s
Channel: Andrew Noble
Description: assume that f and g are differentiable functions with hx gfx suppose that the slope of the tangent line to the graph of f at the point 4 7 is 3 and the slope of the tangent line to the graph 51311

          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 3, and the slope of the tangent line to the graph of g at the point (7, 9) is -2.
Determine the slope of the tangent line to the graph of h at x = 4.

Added by Blake L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andrew Noble

10/11/2022

Step 1

- \( h(x) = g(f(x)) \). - The slope of the tangent line to the graph of \( f \) at the point \( (4, 7) \) is 3. - The slope of the tangent line to the graph of \( g \) at the point \( (7, 9) \) is -2. 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 3, and the slope of the tangent line to the graph of g at the point (7, 9) is -2. Determine the slope of the tangent line to the graph of h at x = 4.