Calculus

Higher-order Derivatives

Second Order Derivatives

         

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

What is the second derivative of f(x)=x9exf(x)=x^{9}e^x with respect to xx?

If f(x)=18x,\displaystyle f(x)=\frac{18}{x}, what is the value of limx1f(x)+18x1?\lim_{x \to 1} \frac{f'(x)+18}{x-1}?

What is the second derivative of y=(x2+2x+7)2?y=(x^2+2x+7)^2?

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

Details and assumptions

lnx\ln x denotes logex\log_e x.

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

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