  # Identify the critical points and ﬁnd the maximum and minimum of the given function on the given interval I.a) G(x) = (1/5)(2x^3 +3x^2−12x); I = [−3,3]b) g(x) = 1/(1+x^2); I = [−3,1]c) f(x) =x/(1+ x^2); I = [−1,4]d) a(t) = cost; I = [π,5π]

Question

Identify the critical points and ﬁnd the maximum and minimum of the given function on the given interval I.

a) G(x) = (1/5)(2x^3 +3x^2−12x); I = [−3,3]
b) g(x) = 1/(1+x^2); I = [−3,1]
c) f(x) =x/(1+ x^2); I = [−1,4]
d) a(t) = cost; I = [π,5π]

check_circleExpert Solution
Step 1

On differentiating the above equation, we get

Step 2

Calculations for the critical value are shown on the board

Therefore, the critical point is at x=1,-2 which lies in the interval I=[-3,3]

Step 3

Now, calculating its maximum and minimum point

• The function has a minimum value at x = a  if f '(a) = 0 and f ''(a) = a po...

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### Calculus 