1 find the equations of the tangents to the curve x 6t2 4 y...

Find the equations of the tangents to the curve x = 6t^2 + 4, y = 4t^3 + 2 that pass through the point (10, 6). Smaller slope? Bigger slope? 2. Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work. (Enter your answers as a comma-separated list of ordered pairs.) x = t^3 - 3t, y = t^2 - 9 horizontal tangent (x, y) = vertical tangent (x, y) =

Transcript

00:01 Hello everyone, so this is the question that we have.

00:03 First, we have to find the equation of tangent to the curve.

00:11 X is equal to 6t square plus 4 and y is equal to 4t cube plus 2.

00:17 That passes through the point 10 .6.

00:22 Part 2, we have to find the points on the curve where the tangent is horizontal or vertical and x is equal to t cube minus 3 t and y is equal to t squared minus 9 so let's jump on to the solution now the curve is given to me as x is equal to 6 t square plus 4 and y is equal to 4 t cube plus 2 and at points 10 comma 6 so differentiation of of x with respect to t is going to be six multiplied by two t which is equal to 12 t and differentiation of y with respect to t is going to be four multiplied by three t square which is 12 t square now combine these y divided by d x is going to be d y divided by d t or divided by d x divided by d t this is going to be 12 t squared divided by 12 t so i get t as the meaning so at these points so point 10 comma 6 so this is going to be x is equal to 10 and y is equal to 6 so i'm going to have x is equal to 10 this implies 6 t square plus 4 is equal to 10 so my t would be equal to plus minus 1 t is equal to plus minus 1.

02:02 Now at y is equal to six this implies 4 t cube plus 2 is equal to 6 4 t cube is equal to 4 t is equal to 4 so t is equal to 1 from here now if i find the slope so slope is equal to d y divided by d x at t is equal to 1 so equation of the tangent could be equation of the tangent is gonna be y minus y 1 is equal to m x minus x1 this is 2 .4 so let's plug it in the values so y minus 6 slope is 1 x minus 10 so i get the equation as y minus 6 is equal to x minus 10 so if i concise this transpose x minus y minus 4 is equal to 0 this is the equation this is the equation now coming on to part 2 of the question.

03:08 So 2.

03:09 X is equal to tq minus 3t and y is equal to t square minus 9.

03:16 So differentiation of these, dx divided by dt would be equal to 3t square minus 3 and d .y divided by dt would be equal to 2t...

Question

Please give Ace some feedback