For finding absolute maximum and minimum values of a function f gives by
$f(x)=2x^3-15x^2+36x + 1 $ on [1, 5].
A. the critical points in (1, 5) are 2 and 3.
B. the absolute maximum value of f on [1, 5] is 29.
C. the absolute minimum value of f on [1, 5] is 24.
D. the absolute minimum values of f on [1, 5] is 20.
E. we evaluate the value of f at critical points and at the end points of the interval [1, 5].
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A, C, E only
$f(x)=2x^3-15x^2+36x + 1$, $x∈[1, 5]$
$f'(x)=6x^2-30x+36=0$
$x^2-5x+6=0$
$(x-2)(x-3)=0⇒x=2,3$ critical points
so $f(1)=2-15+36+1=24$
$f(2)=2×2^3-15×2^2+36×2+1=29$
$f(3)=2×3^3-15×3^2+36×3+1=28$
$f(5)=2×5^3-15×5^2+36×5+1=56$