Simple yet different

Calculus Level 1

You knew that: f ( x ) = a x + 3 f ′ ( x ) = 6 f(x) = ax + 3 \\ f'(x) = 6

Then find the value of a a .

Clarifications:

  • f ′ ( x ) means d d x f ( x ) f'(x) \text{ means } \dfrac{d}{dx}f(x)
  • f ( x ) is a linear polynomial f(x) \text{ is a linear polynomial}


The answer is 6.

Viki Zeta by Viki Zeta , 19, India

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2 solutions

Viki Zeta
Aug 4, 2016

f ( x ) = a x + b ⟹ d d x f ( x ) = d d x ( a x + b ) ⟹ 6 = d d x ( a x ) + d d x ( b ) (Using sum differentiation rule)) ⟹ 6 = a + 0 (Using power rule) ⟹ a = 6 f(x) = ax+b \\ \implies \dfrac{d}{dx} f(x) = \dfrac{d}{dx} (ax + b) \\ \implies 6 = \dfrac{d}{dx} (ax) + \dfrac{d}{dx}(b) \text{ (Using sum differentiation rule))} \\ \implies 6 = a + 0 \text{ (Using power rule)} \\ \implies \fbox{a = 6}

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Why make it look difficult? f (x) is linear so a = f'(x)

Peter van der Linden - 4 years, 10 months ago

∫ f ′ ( x ) = ∫ 6 f ( x ) = 6 x + C = a x + 3 \int f^\prime(x)=\int 6\\f(x)=6x+C=ax+3

Comparing, we have a = 6 a=6 .

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