Find the zeros Find equation of the line tangent to f(x) at (a,b) Find equation

Question

Find the zeros Find equation of the line tangent to f(x) at (a,b) Find equation of the line normal to f(x) at (a,b) Show that f(x) is even Show that f(x) is odd Find the interval where f(x) is increasing Find the interval where the SLOPE of f(x) is increasing Find the minimum value of the function Find the minimum slope of a function Find the critical values Find the inflection points Show that lim_x rightarrow a f(x) exists Show that f(x) is continuous Find the vertical asymptotes of f(x) Find the horizontal asymptotes of f(x)

Explanation / Answer

1) to find zeroes equate f(x) to 0 and solve the equation to fid value of x

f(x)=0

2) find the slope of tangent at x =a by finding the derivative of f at x =a

equation of tangent is

y=b+ [f '(a) (x-a)]

3) slope of normal is -1/f '(a)

equation of normal is

y=b+ [(-1/f '(a)) (x-a)]

4) to show f(x) is even

we have to prove f(-x)= f(x)

5)

to show f(x) is odd

we have to prove f(-x)= -f(x)

6) f(x) is increasing when first derivative greater than zero

f '(x)>0

7)SLOPE of f(x) is increasing when second derivative greater than zero

f "(x) >0

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