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OpenStudy (jmartinez638):
Prove that the function f(x) = 3x^4 +12x-19 must have at least one real zero on the interval (0,3)
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jimthompson5910 (jim_thompson5910):
Can you tell me what the value of `f(0)` is?
OpenStudy (jmartinez638):
-19?
jimthompson5910 (jim_thompson5910):
yes, now how about `f(3)` ?
OpenStudy (jmartinez638):
260
jimthompson5910 (jim_thompson5910):
notice how we change from negative to positive -19 to +260
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jimthompson5910 (jim_thompson5910):
since y changes sign, this means that y has to be 0 at some point (at least once) in the interval
jimthompson5910 (jim_thompson5910):
|dw:1445812049664:dw|
jimthompson5910 (jim_thompson5910):
|dw:1445812060039:dw|
jimthompson5910 (jim_thompson5910):
|dw:1445812095763:dw|
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