Question

A tangent to the parabola y=3x^2 -7x +5 is perpendicular to x + 5y-10 =0. Determine the equation of the tangent .

Answer 1

Things to note for this problem::
- The derivative is the slope of the tangent line on the graph at x.
- The slope of a line perpendicular to y=mx+b is the opposite reciprocal, -m^(-1) = -(1/m)

Answer 2

1st equation: y'=6x-7
2nd equation: y=-1/5x+2
The slope of the function must be 5 for it to be perpendicular
6x-7=5
6x=12
x=2
The tangent line will be perpendicular when x=2

Answer 3

..so, knowing the x-value, we can plug that in to y and find the corresponding y-value for the point on the graph.

y - y1 = m(x - x1); (x1,y1)= (2,y(2)), m = 5

Answer 4

right, they wanted the equation of the line :\

Answer 5

the line should be 5x-y-7=0 as the answer

Answer 6

The point (2,3) will be on the graph and the tangent line

Answer 7

5(2)-3-7=0

Answer 8

y-3=5(x-2)
y=5x-7

Answer 9

same line as your answer

Answer 10

and, unless a form to write the equation in is explicitly stated (or maybe mentioned by teacher), you should not be restricted to writing it in any particular form...