Can someone explain this question?

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2 Answers
Mar 9, 2017

You need to derive your function with respect to t and then solve the resulting equation when you set the derivative equal to zero:

Explanation:

Ok, I can be wrong but your function can be derived as:
f'(t)=e^(2t^2)3*10^(3t-5)ln(10)+10^(3t-5)*4te^(2t^2)
rearranging:
f'(t)=e^(2t^2)*10^(3t-5)[3ln(10)+4t]
Let us set this equal to zero:
e^(2t^2)*10^(3t-5)[3ln(10)+4t]=0
when:
t=-(3ln(10))/4 that makes the square bracket equal to zero....
I think....

Mar 9, 2017

This is what I got.

Explanation:

Given expression is
f(t)=10^(3t-5)xxe^(2t^2)
Using product rule
f'(t)=10^(3t-5)xx(e^(2t^2)xx4t)+e^(2t^2)xxln10xx10^(3t-5)xx3
=>f'(t)=(4t+3ln10)xx10^(3t-5)xxe^(2t^2)

To meet the given condition
(4t+3ln10)xx10^(3t-5)xxe^(2t^2)=0 .....(1)
=>f(t)[4t+3ln10]=0
either f(t)=0
or[4t+3ln10]=0
=>t=-(3ln10)/4 ....(2)

To find roots of f(t)=0,
10^(3t-5)xxe^(2t^2)=0
either 10^(3t-5)=0 .......(3)
or e^(2t^2)=0 ......(4)

From both (3) and (4)
we get t=-oo.
This solution is purely theoretical as such this equation has no solution in real or complex numbers.

As such only possible solution is as given in equation (2)