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

Question

If the derivative of (ax - 5)e3x at x = 0 is - 13, then the value of a is equal to (A) 8 (B) -5 (C) 5 (D) -2

Tardigrade Admin · Accepted Answer

Let y=(a x-5) e3 x On differentiating, we get ∴ (d y/d x)=e3 x(a)+(a x-5) 3 e3 x ((d y/d x))x=0 =e0(a)+(a(0)-5) 3 e0=-13 =1 ⋅ a+(-5) ⋅ 3 ⋅(1)=-13 -13 =a-15 ⇒ a=2

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

8

-5

5

-2

2

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

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

8

-5

5

-2

2

Let y=(ax−5)e3x On differentiating, we get ∴dxdy​=e3x(a)+(ax−5)3e3x (dxdy​)x=0​=e0(a)+(a(0)−5)3e0=−13 =1⋅a+(−5)⋅3⋅(1)=−13 −13=a−15⇒a=2

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

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