What is the equation of the line tangent to f(x)=(x-3)^{2}-x^{2}-3

rabunztr

rabunztr

Answered question

2022-02-10

What is the equation of the line tangent to f(x)=(x3)2x23 at x=5?

Answer & Explanation

Alaina Contreras

Alaina Contreras

Beginner2022-02-11Added 19 answers

Given - 
y=(x3)2x23 
Its first derivative determines its slope
 dy  dx =2(x3)(1)2x 
Slope at x=5 
At x=5; slope = 2(5-3)(1)-2(5)=4-10=-6 
At x=5 the y-co-ordinate is - 
At x=5;y=(53)2523 
y=4-25-3=-24 
(5, 24) is the point on the curve. At that point the slope is -6 
The tangent's mathematical formula is
y=mx+c 
c+mx=y 
c+(-6)(5)=-24 
c-30=-24 
c=-24+30=6 
y=-6x+6

Katrina Patton

Katrina Patton

Beginner2022-02-12Added 11 answers

Though it appears to be a quadratic equation, it is not.
Simplify the function.
y=(x3)2x23
y=x26x+9x23
y=-6x+6
In reality it is linear. Hence a tangent drawn to any point on this curve will coincide with it. The tangent at x=5 is-
y=-6x+6

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