No 1
Diketahui \( f(x) = 2x^3 + (a+1)x + 3 \).
Jika \( f(1) = 9 \), maka nilai \( f'(3) = \) ...
Jawaban
Cari nilai \(a\) terlebih dahulu.
\[ 2(1)^3 + (a+1)(1) + 3 = 9 \]
Diperoleh \( a = 3 \).
Turunan fungsi adalah:
\[ f'(x) = 6x^2 + (a+1) \]
Substitusi \( x = a = 3 \).
\[ f'(3) = 58 \]
No 2
Diketahui \( f(x) = 3x^4 + (a-2)x^2 + 5 \).
Jika \( f(1) = 9 \), maka nilai \( f'(3) = \) ...
Jawaban
Cari nilai \(a\) terlebih dahulu.
\[ 3(1)^4 + (a-2)(1)^2 + 5 = 9 \]
Diperoleh \( a = 3 \).
Turunan fungsi adalah:
\[ f'(x) = 12x^3 + 2(a-2)x \]
Substitusi \( x = a = 3 \).
\[ f'(3) = 330 \]
No 3
Diketahui \( f(x) = 2x^4 + (a+3)x^2 -4 \).
Jika \( f(1) = 4 \), maka nilai \( f'(3) = \) ...
Jawaban
Cari nilai \(a\) terlebih dahulu.
\[ 2(1)^4 + (a+3)(1)^2 -4 = 4 \]
Diperoleh \( a = 3 \).
Turunan fungsi adalah:
\[ f'(x) = 8x^3 + 2(a+3)x \]
Substitusi \( x = a = 3 \).
\[ f'(3) = 252 \]
No 4
Diketahui \( f(x) = 4x^2 + (a-4)x -4 \).
Jika \( f(2) = 10 \), maka nilai \( f'(3) = \) ...
Jawaban
Cari nilai \(a\) terlebih dahulu.
\[ 4(2)^2 + (a-4)(2) -4 = 10 \]
Diperoleh \( a = 3 \).
Turunan fungsi adalah:
\[ f'(x) = 8x + (a-4) \]
Substitusi \( x = a = 3 \).
\[ f'(3) = 23 \]
No 5
Diketahui \( f(x) = 1x^4 + (a-4)x^2 + 2 \).
Jika \( f(1) = 4 \), maka nilai \( f'(5) = \) ...
Jawaban
Cari nilai \(a\) terlebih dahulu.
\[ 1(1)^4 + (a-4)(1)^2 + 2 = 4 \]
Diperoleh \( a = 5 \).
Turunan fungsi adalah:
\[ f'(x) = 4x^3 + 2(a-4)x \]
Substitusi \( x = a = 5 \).
\[ f'(5) = 510 \]