Posted by **Joshua** on Tuesday, April 14, 2009 at 8:52pm.

Let h(x)=16-4x-(x^3)

Find g(96).

My work:

96= 16-4x-(x^3)

(-x^3)-4x-80=0

Using the rational roots theorm, I found that x=-4

so h(-4)=96, therefore g(96)=-4.

Find g'(96).

My work:

g'(96)= 1/(dh/dx at x=-4)

1/((-3(-4)^2)-4)= -1/52

Does this look ok? Also, my math teacher wanted us to find two ways to do this problem and get the same answer. I found one way, but I can't think of another. Any suggestions?

- Calc. -
**Reiny**, Tuesday, April 14, 2009 at 11:18pm
Even though you did not state it, I can see from your work that g(x) must be the inverse of h(x)

Both of your answers are correct.

the alternate way suggested by your teacher might have gone like this:

h(x) = 16-4x-(x^3) is equivalent to

y = 16-4x-(x^3)

then g(x) would be equivalent to

x = 16 - 4y - y^3

I then differentiated this implicitly to get

dy/dx = -1/(4+3y^2)

but remember (-4,96) and (96,-4) are inverse images, so for g'(96) we would use y=-4 in dy/dx to get -1/(4 + 3(16))

= -1/52 as before

## Answer This Question

## Related Questions

- Pre-Calc-Please check - Is this correct? Using Rational Roots Theorem, list all...
- algebra - Factor this polynomial: F(x)=x^3-x^2-4x+4 Try to find the rational ...
- Pre calculus - Find all roots f(x)- x^3+2x^2-15x+30 Factor f(x) completely. I ...
- Pre-Calc-Please check - I have three questions: 1. What is the remainder of (x^3...
- college algebra - Radical and Rational Exponent find roots square roots of 12a^3...
- Math - Find all possible rational roots using the rational root theorem. x^4 - ...
- Math - How to factor x^3 - 3x^2 + 4 =0 Use D'Alembert's Rational Roots Theorem. ...
- ALGEBRA 2 - Use the Rational Root Theorem to list all possible rational roots ...
- algebra - Radical and Rational Exponent find roots square roots of 12a^3/25=6a^3...
- algebra - Radical and Rational Exponent find roots square roots of 12a^3/25=6a^3...

More Related Questions