Question

Find an equation for the tangent line to graph of y=f(x) at x=5 if f(5)=-3 and f'(5)=7. Give the answer in the form of y=mx + b

Answer 1

The equation for the tangent line to the graph of y=f(x) at x=5 is y = 7x - 38.

Step-by-step explanation:

The equation for the tangent line to the graph of y = f(x) at x = 5 can be found using the formula y = f(a) + f'(a)(x - a). Given that f(5) = -3 and f'(5) = 7, we can substitute these values into the formula to get:

y = -3 + 7(x - 5)

Simplifying further, we have:

y = 7x - 38

So, the equation for the tangent line is y = 7x - 38.