Question

f(x)=2 x la a 3-6x+7

Sa se calculeze f(1)+f(derivat de 1) +(f derivat de 2 ori de 1)

Answer 1

$f(x) = 2 {x}^{3} - 6x + 7$

$f(1) = 2 \times {1}^{3} - 6 \times 1 + 7$

$f(1) = 2 - 6 + 7$

$f(1) = 3$

$f'(x) = (2 {x}^{3} - 6x + 7)'$

$f'(x) = (2 {x}^{3} )' - (6x)' + 7'$

$f'(x) = 2 \times ( {x}^{3} )' - 6 \times x' + 0$

$f'(x) = 2 \times 3 {x}^{2} - 6 \times 1$

$f'(x) = 6 {x}^{2} - 6$

$f'(1) = 6 \times {1}^{2} - 6$

$f'(1) = 6 - 6$

$f'(1) = 0$

$f''(x) = (f'(x))'$

$f''(x) = (6 {x}^{2} - 6)'$

$f''(x) = (6 {x}^{2} )' - 6'$

$f''(x) = 6 \times ( {x}^{2} )' - 0$

$f''(x) = 6 \times 2x$

$f''(x) = 12x$

$f''(1) = 12 \times 1$

$f''(1) = 12$

$f(1) + f'(1) + f''(1) = 3 + 0 + 12 = 15$