Question

find , and then find the tangent line to the graph of at x = a. F(x) = 2x^2 ; a = 1.

I know the derivative is 4x but why would the second part be 4x -2? i keep getting plus 2

Answer 1

first evaluate the derivaitve at the given point x=1

Answer 2

f'(1)=4(1)=4

Answer 3

Now we have found out m or slope: 4

Answer 4

also, keep in mind, that when we evaluate the orginal functionat x=1 we get:

f(1)-2(x)^2=2

Answer 5

this means that 2 is our y coordinate

Answer 6

Lets recap, we have been given that x=1, we found y=2, and we also found m or slope=4

Answer 7

lets now plug our info into the equation of a line: y=mx+b

2=4(1)+b

2=4+b
now subtract 4 from both sides to get isolate b, and we get: -2=b

Now, we complete the equation of the line:

y=4x+(-2), lets simplify and we get:


y=4x-2

Answer 8

For some reason when i use the formula to find the instantanous rate of change i keep getting a 4x+2. we have to use that method on the test and i can't figure out how to get that formula to work