Question

If f(x) = 3x² + 12x - 1, -1 ≤ x ≤ 2

f(x) = 37 - x, 2 < x ≤ 3

(a) f(x) is increasing on [-1, 2]

(b) f(x) is continuous on [-1, 3]

(c) f'(2) does not exist

(d) f(x) has the maximum value at x = 2 

Answer 1

Correct option 

(a) f(x) is increasing on [-1, 2]

(b) f(x) is continuous on [-1, 3]

(c) f'(2) does not exist

(d) f(x) has the maximum value at x = 2 

Explanation :

Again function is a algebraic polynomial, therefore, it is continuous at x ∈ (-1, 2) and (2, 3) and for continuity at x = 2.

Again f(x) is increasing on [-1, 2] and is decreasing on (2, 3), it shows that f(x) has a maximum value at x =2.

Therefore, options (a), (b), (c), (d) are all correct.