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#### 06-19 - MESA Challenge Calculus AB

(8 Questions)Question set for the 06/19 challenge.

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Find the second derivative of 1024x^{2} (Hint: second derivative means to just differentiate it again after you find the first derivative)

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Note that f’(x) is the derivative of f(x). If f(x) = 2x^{4} + x^{2} + x + 4, find f’(4).

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Find the derivative of 7y^{3} - 14y^{8} (Hint: differentiate each term individually)

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Finding derivatives of functions (for example 4x^{3}) can be easy at first but quickly becomes more complicated. Simply multiply the coefficient (front number) with the exponent, and then subtract 1 from the exponent. So in our example 4x^{3} we multiply the coefficient (4) by the exponent (3) resulting in 12x^{3}. We then subtracted 1 from the exponent 3, and now have 12x^{2} which is the final answer. Note that the derivative of a constant is just 0.
Find the derivative of 7x^{3}. Enter exponents as ^ (ie 7x^3)

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Find the derivative of 60z (Hint: what does anything to the power of 0 become)

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Note that f’’(x) means the second derivative of f(x). If f(x)=32x^{3}-2x+7, find f’’(3)

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Lastly, find the third derivative of the function f(x)=-9x^{4}-3x^{2}-x+38

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Derivatives and Integrals are concepts that you will make heavy use of in your upcoming Calculus course. Simply put, derivatives are represented by the symbol d and means a little bit of (dx would be a little bit of x and dy a little bit of y). The integral is represented by this symbol: \int and means “the sum of”. Therefore \intdx can be read as the integral of dx. What is dx equal to?

by Frank T