Question

The derivative of the function f is given by f′(x)=−3x+4 for all x, and f(−1)=6. Which of the following is an equation of the line tangent to the graph of f at x=−1? I think it’s y=7x+13, but I could just be delusional

Answer 1

Answer:

You are correct. The answer is $y=7x+13$

Step-by-step explanation:

First, we need to plug in our x value to the derviative's equation to find the slope of the line tangent to the graph, f

$f'(x)=-3x+4\\\\f'(-1)=-3(-1)+4\\\\f'(-1)=3+4\\\\f'(-1)=7$

Now that we have found the slope and have a given point: (-1,6) we can use the point slope formula to find the equation of the line tangent to the graph f.

$y-6=7(x+1)\\\\y-6=7x+7\\\\y=7x+13$