Question

If Δf(x)=eˣ, then f(x) is:​

Answer 1

$\textsf{function , f(x) = (x - 1)e^x }$

$\textsf{differentiating f(x) with respect to x, }$

• $\textsf{f'(x) = d[(x - 1)e^x + 1]/dx }$

• $\textsf{= d[(x - 1)e^x]/dx + d(1)/dx }$

• $\textsf{= e^x d(x - 1)/dx + (x - 1) d(e^x)/dx + 0}$

• $\textsf{= e^x × 1 + (x - 1) × e^x }$

• $\textsf{= e^x + (x - 1)e^x }$

• $\textsf{= e^x(x - 1 + 1) }$

• $\textsf{= xe^x }$

• $\textsf{hence, f'(x) = xe^x }$

for all x > 0

• $\textsf{⇒e^x > e^0 }$

• $\textsf{⇒ e^x > 1 > 0 }$

so, f'(x) = xe^x > 0

• $\textsf{we know, any function f is increasing in (a,b) only when f' > 0 in interval (a, b).}$

• $\textsf{here, f'(x) > 0 in interval, x > 0 }$

• $\textsf{so, f(x) is increasing for all x > 0}$

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Note:-

• $\textsf{kindly view answer from brainly .in for better understanding!}$

Answer 2

xe ^> 0 is right answer okayyy okaaa