A calculus problem by Guilherme Dela Corte

Calculus Level 2

Let f ( x ) = ( x − 2 ) ( x − 4 ) ( x − 8 ) f(x) = (x-2)(x-4)(x-8) . Evaluate the digit sum of f ′ ( f ( 16 ) ) f'(f(16)) .


The answer is 26.

Guilherme Dela Corte by Guilherme Dela Corte , 24, Brazil

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

f ( x ) = ( x − 2 ) ( x − 4 ) ( x − 8 ) = x 3 − 14 x 2 + 56 x − 64 f(x) = (x-2)(x-4)(x-8) = x^3 - 14x^2 +56 x - 64 f ′ ( x ) = 3 x 2 − 28 x + 56 f'(x) = 3x^2 - 28x + 56 f ( 16 ) = 14 ⋅ 12 ⋅ 8 = 1344 f(16) = 14 \cdot 12 \cdot 8 = 1344 f ′ ( 1344 ) = 1344 ⋅ ( 3 ⋅ 1344 − 28 ) + 56 = 5381432 f'(1344) = 1344 \cdot (3 \cdot 1344 - 28) + 56 = 5381432 Σ = 5 + 3 + 8 + 1 + 4 + 3 + 2 ⇒ Σ = 26. \Sigma = 5+3+8+1+4+3+2 \Rightarrow \boxed{\Sigma = 26.}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I did it!

Royette Posadas - 7 years, 1 month ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...