Prime functions

Calculus Level 1

If f ( x ) = 3 x − 5 , f ′ ( x ) = ? \large f(x) = 3x-5, f '(x) = \ ?


The answer is 3.

Yellow Tomato by Yellow Tomato , 17, USA

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2 solutions

Youssef Daoud
Nov 10, 2015

F'(x)=3×1×x^{0} = 3

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Yellow Tomato
Oct 23, 2015

We have f ′ ( a ) = lim ⁡ h → 0 f ( a + h ) − f ( a ) h = lim ⁡ h → 0 ( 3 ( a + h ) − 5 ) − ( 3 a − 5 ) h = lim ⁡ h → 0 ( 3 a + 3 h − 5 − 3 a + 5 ) h = lim ⁡ h → 0 3 h h = lim ⁡ h → 0 3 = 3 \small f '(a) = \lim_{h\to0} \frac{ f( a + h) - f(a) }{h} = \lim_{h\to0} \frac{ (3(a + h) - 5) - (3a - 5)}{h} = \lim_{h\to0} \frac { (3a + 3h - 5 - 3a + 5)}{h} = \lim_{h\to0} \frac{3h}{h} = \lim_{h\to0} 3 = 3

Giving us the answer is 3 \boxed{\boxed{\boxed{3}}}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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