calculus Flashcards
f ‘ (1) =3
The derivative of f when x=1 is 3
The gradient of the tangent to f when x=1 is 3
f’(3)=0
if f(x)=0, there is a stationary point at x=3
g(-4)=7
The point (-4;7) is a point on g
f’(-2) = 3
The derivative of f when x=-2 is 3
The gradient of the tangent to f when x= -2 is 3
f’(2/3) =0
If f(x)=0, there is a stationary point at x=2/3
[ f(3)-f(2) ]. / 3-2
The average gradient of f between x=3 and x=2
f(x) > 0 ; XE (-2;4)
f is positive between X = to -2 and x = 4
f lies above the x axis between x=-2 and x=4
f(x) > 0; XE (-2;4)
f is negative between X = to -2 and x = 4
f lies below the x axis between x=-2 and x=4
f(x) > g(x) ; XE (-2;4)
f is above g between x=-2 and x=4
f is greater than g between x=-2 and x=4
f(x) < g(x); XE (-2;4)
f is below g between x=-2 and x=4
f is less than g between x=-2 and x=4
f’(x) >0 for XE (-1;5]
the derivative/gradient of f is positive from x=-1 to x=5 but not including 5
f is increasing from x=-1 to x=5 but not including 5
f’(x)<0 for XE (-1;5]
the derivative/gradient of f is negative from x=-1 to x=5 but not including 5
f is decreasing from x=-1 to x=5 but not including 5
f’(2)=0, f’’(2)<0
at x=2, the first derivative is 0 and the second derivative is negative
f has a local maximum turning point at x=2
f’’(x) >0
concave up
f’’(x) <0
concave down
