Question

State a non linear function that has an instantaneous rate of change of 3 at x=1

Answer 1

y = x^3

Answer 2

d(f)/dx = 3 at x = 1

let f= a x^2

df/dx = 2 a x

df/dx = 2 a (1) = 3

find a.

Answer 3

I'm a little confused by the way you set it up.

Answer 4

Use f(x) = x^3
df/dx = 3x^2 --> 3(1)^2 = 3

Answer 5

but how did you pull the 3 down from the exponent of x, to become 3x^2

Answer 6

Definition of derivative using power rule

Answer 7

The thing is I haven't learnt derivative's. Its grade 12 advanced functions and I have calculus next semester. So we work with numbers that are close to the point, like 0.01.

Answer 8

Nothing against you, but this is why education in America is failing. They teach you these crummy ways to do stuff like this when there are very easy and purposeful ways to solve problems like this.

Answer 9

But instantaneous rate of change means the derivative. Either @TanteAnna's or my function fits your needs.

Answer 10

@douglaswinslowcooper He doesn't know what that is O_o

Answer 11

Which I'm in awe of. His teachers should teach him calculus instead

Answer 12

We learn Advanced Functions in first semester, then next semester we learn Calculus. There are other ways around this question, that don't involve derivatives. Otherwise my teacher wouldn't of given me this question.