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f(x) = 2x^2+4x for x <0 and 8x^23 for x greater or equal to zero
what would the difference quotient's be for lim x>0 and lim x> 0+?
 one year ago
 one year ago
f(x) = 2x^2+4x for x <0 and 8x^23 for x greater or equal to zero what would the difference quotient's be for lim x>0 and lim x> 0+?
 one year ago
 one year ago

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ash2326Best ResponseYou've already chosen the best response.0
Function is defined as: \[f(x)=2x^2+4x, for\ x<0\] \[f(x)=8x^23. for\ x\ge 0\] for limit 0, f(x) defined for x<0 \[\large \lim_{x \to 0^{}} (2x^2+4x)\] for limit 0+, f(x) defined for \(x\ge 0\) \[\large \lim_{x \to 0^{+}} (8x^23)\]
 one year ago

ash2326Best ResponseYou've already chosen the best response.0
@darkmare do you get this?
 one year ago

darkmareBest ResponseYou've already chosen the best response.0
yes I understand that for the limit of each one that those are used but the questions asks the lim of those values for f prime (0) so those are not the answers they are looking for apparently
 one year ago

sunejaBest ResponseYou've already chosen the best response.0
f(x)=−2x2+4x,for x<0 f(x)=8x2−3.for x≥0 for limit 0, f(x) defined for x<0 lim x→0−(−2x2+4x)= 0 for limit 0+, f(x) defined for x≥0 lim x→0+(8x2−3)=3
 one year ago

ash2326Best ResponseYou've already chosen the best response.0
\[\large f'(x)=\lim_{h \to 0^}\frac{f(xh)f(0)}{xhx}\] to evaluate f'(0), from left hand side ( or to check differentiability) put x=0 in this \[\large f'(x)=\lim_{h \to 0^}\frac{2(xh)^2+4(xh)(2x^2+4x)}{xhx}\] now put x=0 in this, for 0+, use f(x)=8x^23
 one year ago

ash2326Best ResponseYou've already chosen the best response.0
do you get it ? @darkmare
 one year ago

darkmareBest ResponseYou've already chosen the best response.0
yes I do understand that, it is still not accepting it as an answer so I will have to look into it further, perhaps simplify further
 one year ago

ash2326Best ResponseYou've already chosen the best response.0
yeah, you have to simplify it further.
 one year ago
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