Applications of Derivatives
Application of Derivatives
nta_pyq_2025_jan
Grade 12
Question:
The sum of all local minimum values of the function ⎧ 1 - 2x, x < -1 ⎪ ⎪ 1 f (x) = ⎨ (7 + 2|x|), -1 \le x \le 2 3 ⎪ ⎩ ⎪ 11 (x - 4)(x - 5), x > 2 18 is
157 72
131 72
171 72
167 72
Step-by-Step Solution
Key Concept: Apply the core result for monotonicity, tangents and extrema and simplify using the given constraints.
(1) ⎧ 1 - 2x, x < -1 ⎪ ⎪ ⎪ ⎪ ⎪ 1 ⎪ (7 - 2x), -1 \le x \le 2 3 f (x) = ⎨ 1 (7 + 2x) 0 \le x < 2 ⎪ ⎪ 3 ⎪ ⎪ ⎪ ⎪ ⎩ 11 (x - 4)(x - 5), x > 2 18 \therefore Local minimum values at A& B 7 11 - 3 72 168 - 11 157 \Rightarrow \Rightarrow 72 72
Correct Answer: 1