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Let 'a' be a real number such that the function f(x) = ax2 + 6x - 15, x ∈ R is increasing in (-∞, 3/4)  and decreasing in (3/4, ∞) . Then the function g(x) = ax2 - 6x + 15, x ∈ R, has a
  • a)
    local minimum at x = -3/4
  • b)
    local maximum at x = 3/4
  • c)
    local minimum at x = 3/4
  • d)
    local maximum at x = -3/4
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Let a be a real number such that the function f(x) = ax2 + 6x - 15, x ...
We need to find the value of a such that the function f(x) has two distinct roots.

The discriminant of the quadratic equation ax^2 - 6x - 15 = 0 is given by:

D = b^2 - 4ac

= (-6)^2 - 4a(-15)

= 36 + 60a

For the function to have two distinct roots, the discriminant D must be positive. That is,

36 + 60a > 0

Solving for a, we get:

a > -3/5

Therefore, the value of a that satisfies the given condition is any real number greater than -3/5.
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Community Answer
Let a be a real number such that the function f(x) = ax2 + 6x - 15, x ...


∴ g(x) = ax2 - 6x + 15
Local Max. at x = -B/2A

= -3/4
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Let a be a real number such that the function f(x) = ax2 + 6x - 15, x ∈R is increasing in (-∞, 3/4) and decreasing in (3/4, ∞) . Then the function g(x) = ax2 - 6x + 15, x ∈R, has aa)local minimum at x = -3/4b)local maximum at x = 3/4c)local minimum at x = 3/4d)local maximum at x = -3/4Correct answer is option 'D'. Can you explain this answer?
Question Description
Let a be a real number such that the function f(x) = ax2 + 6x - 15, x ∈R is increasing in (-∞, 3/4) and decreasing in (3/4, ∞) . Then the function g(x) = ax2 - 6x + 15, x ∈R, has aa)local minimum at x = -3/4b)local maximum at x = 3/4c)local minimum at x = 3/4d)local maximum at x = -3/4Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let a be a real number such that the function f(x) = ax2 + 6x - 15, x ∈R is increasing in (-∞, 3/4) and decreasing in (3/4, ∞) . Then the function g(x) = ax2 - 6x + 15, x ∈R, has aa)local minimum at x = -3/4b)local maximum at x = 3/4c)local minimum at x = 3/4d)local maximum at x = -3/4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let a be a real number such that the function f(x) = ax2 + 6x - 15, x ∈R is increasing in (-∞, 3/4) and decreasing in (3/4, ∞) . Then the function g(x) = ax2 - 6x + 15, x ∈R, has aa)local minimum at x = -3/4b)local maximum at x = 3/4c)local minimum at x = 3/4d)local maximum at x = -3/4Correct answer is option 'D'. Can you explain this answer?.
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