Question

Find the slope of the tangent line to the graph of f at the given point.

\[f(x) = x^2 + 5x\] at (4, 36)

Please explain, I haven't done this before

Answer 1

I am sure you are a calculus student

Answer 2

There are different approaches. Tell me your status and i will walk you through the procedures

Answer 3

What do you mean by status? and I'm taking Pre-Calculus, yesh.
What are the different approaches? o.o

Answer 4

\(\bf \cfrac{d}{dx}[x^2 + 5x]\implies f'(x)\qquad ({\color{brown}{ 4}},36)\quad thus\quad f'({\color{brown}{ 4}})\)

Answer 5

the approach for pre cal students is that

Answer 6

Find the first derivative of the function and plug in your given x value. The y coordinate is the slope of the line at that point.

Answer 7

evaluate (f(4+h)-f(4))/h

Answer 8

What you get for y when you plug in x is your slope. Maybe I was a bit unclear up there.

Answer 9

@AngelCriner the derivative of the function f(x)
will give you the "function to get the slope" for the f(x)

then you use that "slope function" or derivative, and plug in the "x" given, from (4, 36)

Answer 10

from the resulting simplified expression substitute zero in place of h. The result is the slope of the line.

Answer 11

Then write the equation of the line using slope point form of equation of a line by using (4,36) as a point on the line.