# Calc question?

Let f(x)= 49-x^2

The slope of the tangent line to the graph of f(x) at the point (-7,0) is:

The equation of the tangent line to the graph of f(x) at (7,0) isy=mx+b for

M =

and

B=

### 2 Answers

- PuzzlingLv 72 months ago
I answered a question very similar to this yesterday, but it seems to have been deleted. Also, you have (-7,0) at one place and then (7,0) at the other. I'll show you the method for the first point, but you can easily switch to x=7 to find the slope (m) and y-intercept (b) for the tangent line at the other point.

STEP 1 - Calculate the first derivative.

f'(x) = -2x

STEP 2 - Use that to find the slope at x=-7:

f'(-7) = -2(-7) = 14

m = 14

STEP 3 - Write the equation with the slope included.

y = 14x + b

STEP 4 - Plug in the point (-7,0)

0 = 14(-7) + b

0 = -98 + b

b = 98

Answer:

y = 14x + 98

Check the graph of the function and the tangent line in the link below.

Source(s): https://www.desmos.com/calculator/6xmlpy2uvv - az_lenderLv 72 months ago
f'(x) = -2x,

so M at (-7,0) is 14.

The equation is y = 14x + B,

and the fact that (-7,0) is on the line shows that

B = 0 + 14(7) = 98.