The line tangent to the graph of f at x=5 is y = 1/10x-2. Find d/dx (4f(x)) |x+5

Verified step by step guidance

1. Step 1: Understand the problem. We need to find the derivative of the function 4f(x) at x = 5. The tangent line equation y = \frac{1}{10}x - 2 gives us information about the derivative of f(x) at x = 5.
2. Step 2: Recall that the slope of the tangent line to the graph of f at x = 5 is the derivative of f at that point, f'(5). From the equation y = \frac{1}{10}x - 2, the slope is \frac{1}{10}. Therefore, f'(5) = \frac{1}{10}.
3. Step 3: Use the constant multiple rule for derivatives. The derivative of 4f(x) with respect to x is 4f'(x).
4. Step 4: Substitute x = 5 into the derivative expression. We have 4f'(5).
5. Step 5: Substitute the value of f'(5) from Step 2 into the expression from Step 4. This gives us 4 \times \frac{1}{10}.