Posted by Reza on Friday, February 17, 2012 at 4:19pm.
by critical numbers, they mean
the turning points, (maximim and minimum points)
any points of inflection
the x and the y -intercepts
so for y-intercept, let x = 0
so g(0) = 0, the origin (0,0) is both an x and a y intercept.
for more x-intercepts , let y = 0
x^7 - 7x^5 = 0
x^5(x^2 - 7) = 0
so x = 0 , x = ± √7
g'(x) = 7x^6 - 35x^4 = 0 for max/mins
7x^4(x^2 - 5) = 0
x = 0 or x = ± √5
g''(x) = 42x^5 - 140x^3
= 0 for any points of inflection
14x^3(3x^2 - 10) = 0
x = 0 or x = ± √(10/3)
since (0,0) is both a turning point and a point of inflection, It is neither a maximim nor a minimum
so you have 4 other different x values to sub back into the original equation to find the corresponding y value of the points,
I will leave that up to you
Thank you I really appreciate your help :)
Math - Find the critical numbers of the function. (Enter your answers as a comma...
Calculus - Find the critical numbers of the function. (Enter your answers as a ...
Calculas - Find any critical numbers of the function. (Enter your answers as a ...
Business - Given y = 4x3 − 48x2 + 5. (a) Find the critical values of ...
calculus - Find any critical numbers of the function. (Enter your answers as a ...
help ? - Let f(x) = (x − 3)^−2.Find all values of c in (1, ...
calculus - Let f(x) = (x − 3)−2. Find all values of c in (2...
calculus - For what values of r does the function y = erx satisfy the ...
Math - Find all real solutions of the equation. (Enter your answers as a comma-...
precal - Solve the given equation. (Enter your answers as a comma-separated list...
For Further Reading