How do you find the equation of the

daurialebraslmc

daurialebraslmc

Answered question

2022-04-16

How do you find the equation of the line tangent to f(x)=x2+3x7 at x=1?

Answer & Explanation

star04iks7

star04iks7

Beginner2022-04-17Added 14 answers

Explanation:
Work out the full co-ordinates of the point at x=1 by substituting this value of x into f(x).
f(1)=(1)2+3(1)7=1+37=3
which gives the point
(1, -3).
Now differentiate the function. Multiply each x phrase by the exponent, and then reduce the exponent by 1.
f(x)=2x1+3x0+07x1=2x+3
Find the gradient of the line tangent by inserting your value of x into this derivative, to get
2(1)=3=5.
Put this into the line equation, y=mx+c and then substitute in your values of x and y from the point (1, -3) we found earlier in order to find the value for c.
y=mx+c
y=5x+c
-3=5(1)+c
-3-5=-8=c
Put all of this back into the line equation, and you get
y=5x-8

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