First we have to use the definition for the curve y1 to find m1:
y1=3x2−1y1′=dxdy1=6x=m1
x−3y=41−3y2′=0⟹y2′=m2=1/3For perpendicular lines we havem1m2=−1⟹m1=−1/m2=−1/(1/3)=−3
After we find m1 = -3, we can use the definition for y'1 to find the point (x*,y*) to find the equation of the tangent line:
−3=m1=6x⟹x∗=−1/2;y1∗=3(1/2)2−1=−1/4
At last, we substitute to find the equation of the tangent line:
y−y1∗=m1(x−x∗)y−(−1/4)=(−3)(x−(−1/2))y+(1/4)=−3x−(3/2)y=−3x−47⟹4y+12x+7=0
Reference:
- Thomas, G. B., & Finney, R. L. (1961). Calculus. Addison-Wesley Publishing Company.
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