- #1

Faiq

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## Homework Statement

The curve ##C## has equation

$$y=x^2+0.2sin(x+y)$$

Show that ##C## has no tangent(no point where ##dy/dx=∞##), that is parallel to the y axis.

Attempt

$$1=2x\frac{dx}{dy}+0.2cos(x+y)(1+\frac{dx}{dy})$$

For a tangent to be parallel to y-axis,

$$\frac{dx}{dy}=0$$

$$1=0.2cos(x+y)$$

$$cos(x+y)=5$$

No value of ##(x,y)## exist for which ##cos(x+y)>1##, hence no y-axis parallel tangent.

**Confusion**

Never been taught or encountered ##\frac{dx}{dy}## and thus I am having doubts over the validity of the solution.

Can somebody please verify it?