Differential Calculus

Question

Differentiate f(x)=-x³ - 2x²+1

a. f'(x)=-3x² - 2x

b. f ' (x)= -3x² - 4x

c. f ' (x)= -2x² - 4

d. f'(x)=-3x² + 2x

e. f'(x)=3x² - 2x

Is there a way to do this on the ti-84 calculator? is so provide that please, if not, how would you solve this step by step?

Answer 1

The TI-84 can only find the derivative at a point (x-value). For instance, if the question said:

Find the value of the derivative (or slope of the tangent line) at x = 1 for f(x) = x³ - 2x² +1.

Then you can use the math button, scroll down to "8:nDeriv(" and hit enter. If you have a TI-84 Plus CE you will get a response that looks like this:

In the first lower left block, type in the variable for which you are taking the derivative which is "x". In the second block, type in the function that you are taking the derivative of which is "x³ - 2x² +1". In the lower right block, type in the value of "x" that you are taking the derivative at, which is "1". When filled out, it will look like this:

Then press enter. The calculation is done using numerical estimations and so will have some round off error in it. The value you get when you press enter in this case is -0.999999 but the actual value is "-1" so you must be smart enough to realize that your calculator answer does have some roundoff error and that the correct answer is -1.

If you want the derivative as a function, then, as Mark M. said in his answer, you must use the Power Rule.

Answer 2

Use the Power Rule.