Need calculus help!!?

Question

Which statement is false?

a) A cubic function has at least 1 zero
b) A cubic function has at most 2 turning points
c) A quartic function has at least 1 zero
d) A quartic function has at most 3 turning points

Answer 1

c. Consider f(x) = x^4 + 1. f(x) has no zeroes.

Answer 2

A is true, since imaginary solution come in conjugate pairs, therefore a cubic function can have either 3 real solutions, or 1 real and 2 imaginary solutions.

B is true as well, since the derivative of a cubic function is a quadratic, thus providing two real or two imaginary solutions/turning points (which we don't consider when graphing in the real number system), so a cubic function will have at most 2 turning points (or none if it is continuously increasing or decreasing, i.e. monotonic).

D is true by the same argument as B and A.

C is false. A quartic function does not NECESSARILY have to have a real zero. Draw any 4th degree polynomial going toward infinity in the y direction that doesn't cross the x-axis (or alternatively, going downward toward negative infinity and not crossing the x-axis). If they don't cross the x-axis, they don't have real zeros. There are infinitely many quartic functions that any 3rd grader could draw that have no zeros. There ya go.

Viola!

Answer 3

X^3 has one zero and 2 turning points

Answer 4

i'd say shape is a factor of engineering meaning that a sturdy carry close on math is obligatory, pre-cal is is like algebra to the subsequent point with the Pi chart and understanding approximately radians and perspective measures (which looks significant) yet Calculus is the learn of derivatives, (the slope of a line at a undeniable element) sort of pointless no count what container of workd your going to, in case you inquire from me.