When 
terminates in quadrant III, both 
and 
are negative, and
When 
terminates in quadrant II, 
is negative and 
is positive, so
which gives
Now,
What is the question again
4 x 3+2 x 2+ x −7=0 ... 3.3 Find roots (zeroes) of : F(x) = 4x3+2x2+x-7. Polynomial Roots Calculator is a set of methods aimed at finding values of x
Answer:
-1.
Step-by-step explanation:
First find the derivative of f(x):
f'(x) = -3x^2 + 12x - 9 = 0 for a maximum or minimum.
-3(x^2 - 4x + 3) = 0
(x - 1)(x - 3) = 0
x = 1, 3.
To find which gives a relative maximum we find the second derivative:
f"(x) = -6x + 12
When x = 1 f"(x) = 6, positive.
when x = 3, f"(x) = -6, negative.
So x = 3 gives a maximum value of f(x).
f(3) = -(3)^3 + 6*(3)^2 - 9(3) - 1 = -1 (answer).
