If f(x)=2x^(2)-x^(3), find f^(')(x),f^('')(x),f^(''')(x), and f^((4))(x)
f^(')(x)
f^('')(x)=
f^(''')(x)=
f^((4))(x)=
Graph f_(t)f^('),f^(''), and f^(''') on a common screen.
i)
i)
(i
Are the graphs consistent with the geometric interpretations of these derivatives?Let f(x)=x^(3).
(a) Estimate the values of f^(')(0),f^(')((1)/(2)),f^(')(1),f^(')(2), and f^(')(3) by zooming in on the graph of f. (Round your answers to one decimal place.)
f^(')(0)=
f^(')((1)/(2))=
f^(')(1)=
f^(')(2)=
f^(')(3)=
(b) Use symmetry to deduce the values of f^(')((-1)/(2)),f^(')(-1),f^(')(-2), and f^(')(-3). (Round your answers to one decimal place.)
f^(')((-1)/(2))=
f^(')(-1)=
f^(')(-2)=
f^(')(-3)=
(c) Use the values from parts (a) and (b) to graph f^(').
C
(i)
(i)
(d) Guess a formula for f^(')(x). Use the definition of the derivative to verify that your guess is correct.
f^(')(x)=(x^(4))/(4)
f^(')(x)=3x
f^(')(x)=3x^(2)
f^(')(x)=3x+2
Need Help?Find the first and second derivative of the function.
G(r)=sqrt(r)+
oot(7)(r)
G^(')(r)=
G^('')(r)=
Need Help?Find the first and second derivative of the function.
G(r)=sqrt(r)+
oot(7)(r)
G^(')(r)=
G^('')(r)=
Find the first and second derivative of the function
G(r)=Vr+Vr
=(,
=(a.
