Question

Given f(x)=−4x^2−7x, determine the points where
(a) the curve intercepts the x− axis;
(b) the tangent line to the curve is horizontal.

Answer 1

(a) f(x) = 0
(b) df(x)/dx = 0

Answer 2

i'm sorry can u explain? it?

Answer 3

what can you tell me about the x axis? what is the value of y on the x axis?

Answer 4

zero is the value.

Answer 5

right. so at the point that the curve intercepts the x axis, what is the value of f(x) ?

Answer 6

0? is it?

Answer 7

but how do we find the value for x?

Answer 8

yes.

Answer 9

if f(x) = 0, that means-4x^2 - 7x = 0 since f(x) = -4x^2 -7x

Answer 10

so x=0 or x=7/-4?

Answer 11

you have to do the calculations yourself. I am not going to do your calculations for you. plug your equation into the roots for ax^2 + bx +c = 0

Answer 12

why? cant we just factor (-4x^2-7x) and get x(-4x-7) then find the value for x?

Answer 13

sure, that works too.

Answer 14

so, what the points where the curve intercepts the x axis?

Answer 15

is it (7/-4,0)

Answer 16

but i dont think thats right.

Answer 17

why not? also, you are missing one more point

Answer 18

(0,0) is the other one

Answer 19

yes.

Answer 20

ok i get it! so for me we just plug in 0=-8x-7?

Answer 21

huh?

Answer 22

you mean for the second part? yes,

Answer 23

yes i meant to say for "b)"

Answer 24

Thank you! so much!

Answer 25

happy to help