Question

finding the derivative and the tangent line

Answer 1

@.Sam.

Answer 2

Have you did the derivative?

Answer 3

yeah i did but im not sure if it is correct

Answer 4

i got -9x^(-1/2)

Answer 5

but it is wrong

Answer 6

You did the dervative wrong,
\[f(x)=7x-32\sqrt{x}\]
Do you get
\[f'(x)=7-\frac{32}{2\sqrt{x}}\]

Answer 7

yes i got that now

Answer 8

Simplify it, and then it says x=a, and 'a' is 4, so
\[=7-\frac{16}{\sqrt{4}}\]
Simplify

Answer 9

is it -1?

Answer 10

Yep

Answer 11

so is that the tangent of the line? that doesnt seem like the equation

Answer 12

You got the gradient/slope, -1, now you need is a set of coordinates and construct yourself an equation of tangent using the point-slope form.

Answer 13

I am confused, i get the slope but how do i get the points?

Answer 14

You could find the y-coordinate by letting f(x)=y
\[y=7x-32\sqrt{x}\]
When x=4,
y=-36

m=-1, (4,-36)
Sub in

\[y-y_1=m(x-x_1)\]

Answer 15

what do i plug in for x1 and y1?

Answer 16

(4,-36)

Answer 17

ok how about for x and y?

Answer 18

never mind that was a stupid question

Answer 19

x and y are the variables for the new equation

Answer 20

lol

Answer 21

y=-x-32?

Answer 22

thank you very much @.Sam.

Answer 23

You're welcome