Question

differentiate:
a)f(x)=(x^2+2)(2x^3-5x^2+4x)

b)Describe in own words how you would determine the instantaneous rate of change of a function using the methods.

Answer 1

Product rule:
\[(f(x)g(x))'=f'(x)g(x)+f(x)g'(x)\]
Tell me what you get and we can work through it.

Answer 2

i get (x^2+2)(6x^2-10x+4)+(2x)(2x^3-5x^2+4x)
=6x^4-10x^3+4x^2+12x^2-20x+8+4x^4-10x^3+8x^2
=10x^4-24x^3-20x+8
=40x^3-72x^2-20

Answer 3

wrong?

Answer 4

or is it 40x^3-60x^2+48x-20

Answer 5

Assuming you did your algebra correctly that should be right. The derivatives were taken correctly.

Answer 6

how do i answer the second question?

Answer 7

Instantaneous rate of change is the interpretation of the derivative of a function at a point or value of the independent variable. The derivative is the limit of the average rate of change between a fixed point and the other point of the curve which is closer to that point(fixed point). If for a function, limit exists, then it is defined as the instantaneous rate of change at that fixed point.
Would this be right??

Answer 8

That's a very nice, and quite accurate, interpretation. Wow. You've got good grasps of both the subject matter and the language used to describe it.

Answer 9

would you give 3 marks for that?

Answer 10

I'm a teacher myself, and yes, I would give you 3 points for that response.

Answer 11

what is secant method and how to use?