Let for real .

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

p(x)=e^{0.4x}-x^{2}-1

for real

x

. (a) Evaluate

p(-1)

p(0)

, and

p(3)

. (b) Using the results from part (a), identify two disjoint open intervals, each of length 1, on which

p

must attain the value

0

. Explain why each interval you provide satisfies the required condition. (c) Argue whether

p

can have more than two real zeros. Support your conclusion with appropriate reasoning involving derivatives or the general shape of the function.