Can't solve this: Let F(x)=int[1,x](3t^3-x^2 t)dt; find f'(x), min of F(x)

[Kochu]

3. Let \(\displaystyle \displaystyle F(x)\, =\, \int_1^x\, (3t^3\, -\, x^2 t)\, dt.\)

. . . . .(1) Calculate \(\displaystyle F'(x).\)

. . . . .(2) Find the minimum of \(\displaystyle F(x).\)

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I tried to use the fundamental theorem of calculus directly F´(x)= 3x^3-x^3 but it was wrong.

 

[Deleted member 4993]

3. Let \(\displaystyle \displaystyle F(x)\, \int_1^x\, (3t^3\, -\, x^2 t)\, dt.\)

. . . . .(1) Calculate \(\displaystyle F'(x).\)

. . . . .(2) Find the minimum of \(\displaystyle F(x).\)

I tried to use the fundamental theorem of calculus directly F´(x)= 3x^3-x^3 but it was wrong.

Do you know Liebniz's rule?