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Let $q(x)$ be a continuous function which is defined for all real numbers. A portion of the graph of $q^{\prime}(x)$, the derivative of $q(x)$, is shown below.


On which of the following interval(s) is $q(x)$ increasing?

  1. $(0,2)$
  2. $(2,4)$
  3. $(7,9)$
  4. None of these
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Option B and C are correct.

A function $f(x)$ is increasing in a interval $(a,b)$, iff it’s derivative $f’(x)$ is positive in the interval $(a,b)$.

Given the options, $q’(x)$ is negative in the interval $(0,2)$, but positive in the intervals $(2,4)$ and $(7,9)$.
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here have to check where graph is positive it means it’s inreasing

A is false as it’s negative ….prev i also ticked a,b as ans

but now it’s cleared like hv to check positive then it implies tht  it’s increasing
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We define the increasing and decreasing intervals using the first derivative of the function f(x) as:

  • If f'(x) ≥ 0 on an interval I, then I is said to be an increasing interval.
  • If f'(x) ≤ 0 on an interval I, then I is said to be a decreasing interval.
  • The function is constant in an interval if f'(x) = 0 through that interval.

Therefore the answer is B and C

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