№5
f(x) = 2x² + 3x + 1
x(0) = -3
y(кас) = f(x0) + f '(x0)(x-x0)
f(x) = 2x² + 3x + 1
f(x0) = f(-3) = 2*9+3*(-3)+1 = 18-9+1=10
f '(x) = 4x +3
f '(x0) = f(-3) = 4*(-3) +3 = -12+3 = -9
y(кас) = 10 -9(x+3) = 10-9x-27 = -9x-17 в точке х0 = -3
№ 4
f(x) = x³ -3x²
f '(x) = 3x²-6x
f '(x) = 0
3x²-6x=0
3x(x-2)=0
3x = 0 или х-2=0
x(1) =0 ; x(2) = 2
f '(0) = 0 и f '(2) = 0
№1
а) f(x) = 2x^{5} + x^{7} - 12
f '(x) = 10x^{4} + 7x{6}
б) f(x) = 7x^{-3} + sinx = 7/x^{3} + sinx
f '(x)= cos x - 21/x^{4}
в) f(x) = ln (4x+3)
f '(x) = 4 / (4x+3)
г) f(x) =e^{x} (2x+5)
f '(x) = (2x+5)e^{x} + 2e^{x}