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  4. If the derivative of (ax - 5)e3x at x = 0 is - 13, then the value of a is equal to

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Q. If the derivative of $(ax - 5)e^{3x}$ at $x = 0$ is $- 13$, then the value of $a$ is equal to

KEAMKEAM 2016Continuity and Differentiability

Solution:

Let $y=(a x-5) e^{3 x}$
On differentiating, we get
$\therefore \frac{d y}{d x}=e^{3 x}(a)+(a x-5) 3 e^{3 x}$
$\left(\frac{d y}{d x}\right)_{x=0} =e^{0}(a)+(a(0)-5) 3 e^{0}=-13 $
$=1 \cdot a+(-5) \cdot 3 \cdot(1)=-13$
$-13 =a-15 \Rightarrow a=2 $