## IB Math Studies Second Derivative

Number and algebra, Descriptive statistics, Logic, sets and probability, Statistical applications, Geometry and trigonometry, Mathematical models, Introduction to differential calculus.

### IB Math Studies Second Derivative

IB Mathematical Studies SL – Calculus, Derivatives, Differentiation, Second Derivative

Can anyone help me to find the second derivative f’’(x) of the following functions?

a) $f(x)=x^3+2x^2+7x-10$

b) $f(x)=2x^5+3x^4-5x^3+4x^2+9x-14$

c) $f(x)=\frac{1}{x}$

Thanks
hill

Posts: 0
Joined: Tue Mar 19, 2013 8:49 pm

### Re: IB Math Studies Second Derivative

IB Mathematical Studies SL – Calculus, Derivatives, Differentiation, Second Derivative

The Second Derivative is the first derivative of the first derivative!

a) $f(x)=x^3+2x^2+7x-10$

the first derivative is:
$f'(x)=3x^2+4x+7$

and the second derivative is:
$f''(x)=6x+4$

b) $f(x)=2x^5+3x^4-5x^3+4x^2+9x-14$

the first derivative is:
$f'(x)= 10x^4+12x^3-15x^2+8x+9$

and the second derivative is:
$f''(x)= 40x^3+36x^2-30x+8$

c) $f(x)=\frac{1}{x}=x^{-1}$

the first derivative is:
$f'(x)= -1x^{-2}$

and the second derivative is:
$f''(x)= 2x^{-3}=\frac{2}{x^3}$

Hope these help!!
elizabeth

Posts: 0
Joined: Mon Jan 28, 2013 8:09 pm

### Re: IB Math Studies Second Derivative

Thanks Elisabeth!!
hill

Posts: 0
Joined: Tue Mar 19, 2013 8:49 pm