this week in calculus we reviewed and are getting ready for our exam by doing our beastfull study guide.
Things on the study guide that i understand include the first and second derivitive test and optimization.
First Derivative test-determine if it is continious and differentiable on the interval. If it is then you take the first derivitve and set equal to zero. Once set equal to zero solve for x and set your x into intervals. Then from there you plug in and find your max and mins.
Second derivative Test- determine if it is continious and defferentiable, if not then it doesnt work. take first derivative then take the second derivative and set the second equal to zero. Solve for x. Set up your x intervals and then plug in from within those intervals into the equation. Then you find your concavity, concave up and concave down.
Optimization - determine primary equation and then determine secondary and solve the secondary for an equation. Once solved plug it into the primary equation and then solve for that variable and then take the derivative and set equal to zero. Once set equal to zero you then plug back into the primary equatin and get your answers.
I still dont fully understand how to look at a graph and determine the derivative and the lim. The graph stuff messes me up.
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i'm not sure about the derivatives but for the limits of a graph you look at the graph and if it says what is the limit of x->1 then you'll look at the whole graph, first looking at the nigative side of the graph along the vertical axis of x = 1 and then at the positive side:...
ReplyDeleteso if you have like a jump at x=1 then where the 1 is going towards the negative side whereever it lands on the x=1 axis then that's the limit of 1(-)
however, if you have a jump at x=1 and where the 1 is going towards the positive side wherever it lands on the x=1 axis then that's the limit of 1(+)
then if 1(-) and 1(+) are the same then that's the limit of 1 however if they are not the same then the limit is DNE [it does not exist]
okay..for derivatives of graphs you have to know that a graph of a (x^2) is a parabola, then (x^3) is a parabola with one hump..and the higher the number the more humps..
ReplyDeleteso when you take the derivative, the exponent is subtracted by one..so if you had a parabola, the exponent after the derivative would be one, making it a diagonal line..and if you had a diagonal line, then the derivative would be a horizontal line.
when you take a derivative your exponent is subtracted by 1 so when you have a parabola the exponent would be 1
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