Question

Let f(x)= {9 sin (x)}{x+1} . Find the slope of the line tangent to f(x) at x=0 . slope = ____-

Answer 1

The slope of the line tangent to the function f(x) at x=0 is 9.

Step-by-step explanation:

To find the slope of the line tangent to the function f(x) at x=0, we need to calculate the derivative of f(x) with respect to x and evaluate it at x=0. The derivative of f(x) is given by:

f'(x) = 9 cos(x)(x+1) + 9sin(x)(1) = 9(x+1) cos(x) + 9sin(x)

Evaluating f'(x) at x=0, we get:

f'(0) = 9(0+1)cos(0) + 9sin(0) = 9(1)(1) + 0 = 9

Therefore, the slope of the line tangent to f(x) at x=0 is 9.