*cruisin’ down the highway in your Bentley*

*going in a straight line, feelin’ like a G*

*checkin’ out your speed, set at 63*

*can also use a graph to calculate velocity*

*say x-axis is time and y is position*

*velocity easy to get, don’t you listen*

*just find change of y over change of x slope is rise over run or m…that’s a bet*

*don’t know what I mean, review on my mic*

*a linear function is like that cruise down the pike start at b, where time is zero money y=mx+b, don’t laugh, this ain’t funny*

*Chorus:**we ain’t drivin’ in a straight line on our next trip*

*slowin down speeding up as you zip*

*velocity is changing, with acceleration bro*

*need to use calculus to find out all the info*

*non-linear functions are mad confusing*

*this ain’t no simple graph like y=mx+b*

*in a linear function, or a straight line slope is constant each and every time but we aint drivin’ in a straight line on our next trip slowin’ down speeding up as you zip velocity is changing with acceleration bro need to use calculus to find out all the info crazy lookin graph with all them curves slope is always changing, that’s my word gotta calculate the derivative at any point on the line, need to find what it is*

**Chorus***y always relates to x as a function also called f(x) at this juncture pick any point on the curve at x y coordinate will be f(x) pick another point along the way, yessur tiny distance h from where you were that x coordinate’s gonna be x+h y will be f(x+h) slope is change in y over change in x m=f(x+h)-f(x) over (x+h)-x almost done now and you’ll be set*

**Chorus***that’s numerator over h bro but now we gotta make that tiny h zero can’t have a zero in denom so here’s what we do find limit as h approaches zero dude it ain’t really hard, think more, don’t complain calc is the study of instantaneous rate of change accurate measurements are infinitesimally small listen to my rhyme, ya ‘bout to know it all for finding slope now need a derivative can find it at any point with the function they give f(x) = x*

^{2}, piece of cake to find derivative just plug in for pete’s sake derivative is dy/dx or f’(x) same thing, none is better than the rest that’s (x+h)

^{2}– x

^{2}over h equals x

^{2}+ 2xh + h

^{2}– x

^{2}over h equals 2x+h ya see but h is approachin’ zero, whatd’a think G derivative of x

^{2}is 2x finally

**Chorus**