Higher-order Derivatives

Second Order Derivatives

Suppose that $f(x)=xe^{ax+b}, f'(0)=3, f''(0)=6,$ where $a$ and $b$ are constants. What is $a+b?$

4+e^3

4+\ln 3

1+e^3

1+\ln 3

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by Brilliant Staff

What is the second derivative of $f(x)=x^{9}e^x$ with respect to $x$ ?

e^x(x^{9}+18x^{8}+72x^{7})

e^x(18x^{8}+72x^{7})

9x^{7}e^x

72x^{7}e^x

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by Brilliant Staff

If $\displaystyle f(x)=\frac{18}{x},$ what is the value of $\lim_{x \to 1} \frac{f'(x)+18}{x-1}?$

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by Brilliant Staff

What is the second derivative of $y=(x^2+2x+7)^2?$

4x^2+8x+28

12x^2+24x+36

4x^2+24x+36

4x^2+8

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by Brilliant Staff

$f(x)=xe^{ax+\ln b}$ , where $a$ and $b$ are constants. If $f'(0)=7$ and $f''(0)=126$ , what is the value of $a+b$ ?

Details and assumptions

$\ln x$ denotes $\log_e x$ .

$f''(x)$ denotes the second derivative of $f(x)$ .

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by Brilliant Staff

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